Other work [1]}, [2]}, [3]} has explored penalized matrix decomposition incorporating sparsity or total variation penalties in related contexts. An important strength of our proposed approach is the focus on highly scalable patch-wise computations (similar to CaImAn); this leads to fast computations and avoids overfitting by (implicitly) imposing strong sparsity constraints on the spatial matrix \(\mathbf {U}\) . We also employ a constrained optimization approach using the trend-filtering (TF) penalty, which is more flexible e.g. than the sparse convolutional temporal penalty used in [1]}, since the constrained TF approach doesn't require us to fit a specific convolutional model or to estimate any Lagrange multipliers for the sparsity penalty.
